Taxiway D to Runway 27R crosses runway 35. Is asking the ground controller if I am cleared to cross runway 35 unnecessary due to the "follow" command?

No. you definitely should have asked if you were cleared to cross runway 35. In fact, it should have been explicitly stated by the controller, per the 7110.65U, 3-7-2.d:

Quote

d. When an aircraft/vehicle is instructed to “follow” traffic and requires a runway crossing, issue a runway crossing clearance in addition to the follow instructions and/or hold short instructions, as applicable.